**1. Homework Statement**

In n>2 is a Carmichael number and p/n is an odd prime, then show that gcd(p-1,n-1) >1

**2. Homework Equations**

**3. The Attempt at a Solution**

This is what I did, but I am not sure if its right:

Choose an a coprime to n and that does not divide p (2 will work because p is prime and carmichael numbers are odd).

Then a

^{p-1}[tex]\equiv[/tex]1 (mod p) (by Fermats Little Theorem) and a

^{n-1}[tex]\equiv[/tex]1 (mod n) by definition. This implies that a

^{n-1}[tex]\equiv[/tex]1 (mod p) because p/n.

So to finish can I just say that because a

^{p-1}[tex]\equiv[/tex]1 (mod p) and a

^{n-1}[tex]\equiv[/tex]1 (mod p) this implies that a

^{p-1}

^{^some integer}=a

^{n-1}, and so (p-1)/(n-1)?

Any help would be greatly appreciated. Thanks guys.